Rozwiąż równanie

[kamil665]

\(\displaystyle{ ( x^2+2x)^2-x^2= 0}\)

[Lbubsazob]

3 wzór skróconego mnożenia \(\displaystyle{ a^2-b^2=(a-b)(a+b)}\)
\(\displaystyle{ \left(x^2+2x \right)^2-x^2=0 \\
\left(x^2+2x-x^2 \right) \left(x^2+2x+x^2 \right) =0 \\
...}\)

[JakimPL]

\(\displaystyle{ ( x^2+2x)^2-x^2 = x^4+4 x^3+3 x^2 = x^2 (x^2+4 x+3)}\)

Teraz tylko rozłożyć nawias.

[Deixis]

\(\displaystyle{ (x ^{2} + 2x) ^{2} - x ^{2} = 0}\)
Wzór skróconego mnożenia:
\(\displaystyle{ (a + b) ^{2} = a ^{2} + 2ab + b ^{2}}\)
\(\displaystyle{ x ^{4} + 4x ^{3} + 4x ^{2} - x ^{2} = 0}\)
\(\displaystyle{ x ^{4} + 4x ^{3} + 3x ^{2} = 0}\)
\(\displaystyle{ x ^{2}(x ^{2} + 4x + 3) = 0}\)
\(\displaystyle{ x ^{2} = 0 \cup x ^{2} +4x + 3 = 0}\)
\(\displaystyle{ x= 0}\)
\(\displaystyle{ delta = 16 - 12 = 4 \sqrt{delta} = 2}\)
\(\displaystyle{ x = -3 \cup x= -1}\)

Odp:
\(\displaystyle{ x = -3; x = -1; x = 0}\)

[Mariusz M]

3 wzór skróconego mnożenia \(\displaystyle{ a^2-b^2=(a-b)(a+b)}\)
\(\displaystyle{ \left(x^2+2x \right)^2-x^2=0 \\
\left(x^2+2x-x^2 \right) \left(x^2+2x+x^2 \right) =0 \\
...}\)

Ten wzór to jest trochę źle zastosowany

\(\displaystyle{ \left(x^2+2x \right)^2-x^2= \left(x^2 +2x-x\right) \left(x^2+2x+x \right) =0}\)

\(\displaystyle{ \left(x^2-x \right) \left(x^2+3x \right)=0}\)

\(\displaystyle{ x^{2} \left(x-1 \right) \left(x+3 \right)=0}\)